U2 Expect big things from the world’s biggest band

With previous jaunts that included the sensory overload of “ZooTV” and coming on stage via a huge lemon, the Irish band has set the bar pretty high.

Its latest invention for the “360 ∞ Tour,” which comes to Pittsburgh’st Heinz Field on Tuesday, is a space oddity, indeed. Coined The Claw, the four-legged, 170-foot-tall structure sits atop the band’s already gigantic stage like a “Super 8”-esque alien ship.

But though the presentation is futuristic, U2’s set list, recently witnessed at a humid-yet-sold-out Miami stadium show, is mostly about the past.

In fact, Bono and company start off the show with an “Achtung Baby” tribute, including the high-powered opener “Even Better Than the Real Thing,” the guitar-driven “Until the End of the World,” the raucous “The Fly” and the sensuous “Mysterious Ways.” The band’s definitive alternative album receives a 20-year reissue later this year, with U2 apparently wanting to preach the fact to its choir.

As for U2 in 2011, there’s little doubt that the biggest-band-in the-world tag now belongs to these Irish gents (Bono, The Edge, Larry Mullen, Adam Clayton Jr.), which for two years has watched its “360 ∞ Tour” become the most successful outing ever. It should be noted the group had to postpone its current leg for a year due to Bono’s back surgery in 2010.

Therefore, these are interesting times for the band, which for the first time in 30 years is supporting an album without a clear-cut hit single. In theory, the “This Is Not a Rebel Song” outfit is still touring its latest effort, 2009’s “No Line on the Horizon,” an album that barely went platinum and appeared to do so on the strength of the U2 name alone — and not a hit song. The album’s lead single, “Get Your Boots On,” didn’t catch fire like its predecessor, “Vertigo,” from “How to Dismantle an Atomic Bomb.”

Still, a little bump in the road of success won’t stop the juggernaut that is U2, with Bono and The Edge showing off their rock-star stage presence nightly. Whether it is Bono going operatic on the obscure “Miss Sarajevo” from “The Passengers” soundtrack or The Edge’s bombastic, classic rock riff “Sunday Bloody Sunday,” the band overwhelmingly proves its Rock Hall Inductee status. Incidentally, the latter song, which for decades represented the violence in the group’s homeland, is transformed of late into an instant anthem for civil rights around the globe. It’s an odd sight to see Arabic writing (related to the recent Middle East uprisings) shown on video screen greeted with cheers from more than 72,000 Americans.

Then again, the idea of uniting not dividing, always has been U2’s modus operandi. From its Martin Luther King-inspired “Pride,” which still is goose-bump producing today, to the humanizing “One,” the band always had an agenda of turning hate into tolerance.

Considering any “No Line on the Horizon” momentum is long gone — the album came out a year and a half ago — the band is offering fans something special, digging into its past for obscure songs such as “Batman Forever” soundtrack single “Hold Me, Thrill Me, Kiss Me, Kill Me,” “Zooropa” (which was never played stateside) and the aforementioned “Miss Sarajevo.”

Also, the band’s monster 1987 album “The Joshua Tree” still is represented with its big three (“Where the Streets Have No Name,” “I Still Haven’t Found” and “With or Without You”).

Looking ahead for U2, the outfit is at a crossroads: Does the group return to its hit rock-single past (which is hard to do these days) or become the Rolling Stones, releasing albums for diehards but whose appeal is solely based in its legend and catalog? The fact the group’s current tour is sold out, it appears either scenario suffices for fans. Any day seeing U2 live is a, well, “Beautiful Day.”